{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 线性模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 样本准备"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.array([0.9,0.1])\n",
    "x2 = np.array([0.2,0.8])\n",
    "y1 = 1\n",
    "y2 = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.9, 0.1]), array([0.2, 0.8]), 1, -1)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1,x2,y1,y2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w=np.array([0.3,0.3])\n",
    "b=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型定义"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x):\n",
    "    y = np.sum(x*w)+b\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.980313703831305"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 求解模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 转化为求最小值的过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def loss(x,y):\n",
    "    error=model(x)-y\n",
    "    loss_value=error*error\n",
    "    return loss_value\n",
    "\n",
    "# error = w*x + b \n",
    "#  loss = error^2\n",
    "#  dloss/dw = 2*error*x\n",
    "#  dloss/db = 2*error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48999999999999994"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss(x1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6900000000000002"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss(x1,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_all=3.784749096278132\n"
     ]
    }
   ],
   "source": [
    "loss_all = loss(x1,1)+ loss(x2,1)\n",
    "print(\"loss_all=%s\"%(loss_all))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 用梯度下降法求loss的最小值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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      "loss_value=0.0008317006466355109,predict=[0.9801786296142901,-0.979052114124141],gt=[1,-1]\n",
      "loss_value=0.0008300773510994331,predict=[0.9801979825254217,-0.9790725669267364],gt=[1,-1]\n",
      "loss_value=0.0008284572238768544,predict=[0.98021731654103,-0.9790929997599118],gt=[1,-1]\n",
      "loss_value=0.0008268402587839555,predict=[0.9802366316795638,-0.9791134126431642],gt=[1,-1]\n",
      "loss_value=0.0008252264496489415,predict=[0.9802559279594543,-0.9791338055959722],gt=[1,-1]\n",
      "loss_value=0.0008236157903120943,predict=[0.9802752053991144,-0.9791541786377949],gt=[1,-1]\n",
      "loss_value=0.0008220082746256939,predict=[0.9802944640169389,-0.9791745317880731],gt=[1,-1]\n"
     ]
    }
   ],
   "source": [
    "for i in range(1000):\n",
    "    loss_value=0\n",
    "    loss_value= loss_value + loss(x1,1)\n",
    "    loss_value= loss_value + loss(x2,-1)\n",
    "    print(\"loss_value=%s,predict=[%s,%s],gt=[%s,%s]\"%(loss_value,model(x1),model(x2),1,-1))\n",
    "    # 按照梯度的公式，学习率定为0.001\n",
    "    w[0] = w[0] - 0.001 *(2*(model(x1)-1)*x1[0]+2*(model(x2)--1)*x2[0])\n",
    "    w[1] = w[1] - 0.001 *(2*(model(x1)-1)*x1[1]+2*(model(x2)--1)*x2[1])\n",
    "    b = b-0.001 * (2*(model(x1)-1) + 2*(model(x2)--1))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.06064152, -0.71268245]), -0.25151118757965946)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6317979368077278, -0.6095288405930028)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(x1),model(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 逻辑斯特回归分类模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def logistic(x):\n",
    "    h = np.sum(x*w) + b\n",
    "    y = 1/(1+np.exp(-h))\n",
    "    return y\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.980313703831305, -0.9791948650662281)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(x1),model(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7271704576033493"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27305156923702895"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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